Here, we address these challenges and develop a procedure to witness entanglement using trRIXS. As a brief summary of the main results, we quantify the impact of finite core-hole lifetime on the evaluation of dynamical structure factor, develop a self-consistent protocol to calculate the instantaneous QFI, and assess the multipartite entanglement dynamics using the QFI and appropriate theoretical bounds. Through this procedure, we focus on the study of light-induced entanglement when a system is close to a phase boundary and choose a one-dimensional (1D) extended Hubbard model (EHM). The EHM under consideration, with repulsive on-site interaction and attractive nearest-neighbor interaction, has been recently identified as the underlying microscopic model for 1D cuprate chains (e.g., Ba\(_{2-x}\) Sr\(_x\) CuO\(_{3+\delta }\) ) [1]}. By comparing its dynamics with that of a pure Hubbard model, we find that the nonlocal interaction plays a crucial role on the nonequilibrium entanglement enhancement.
